A modulated optical reflectance (MOR) technique was first developed by Rosencwaig in 1985 when it was found that thermal waves could be detected using the change in optical reflectivity due to the change in surface temperature See A. Rosencwaig, J. Opsal, W. Smith, D. Willenborg, Detection of thermal waves through optical reflectance, Applied Physics Letters, 46 (1985) 1013-1015. This measurement technique utilizes two lasers. One laser is used to produce a transient thermal response in the sample (pump), and the second laser (probe) is used to detect the thermal response based on its reflection off the sample's surface. MOR measurements are largely separated into two categories in which the pump and probe beams are either pulsed or continuous. In both cases the pump beam is typically modulated periodically and amplitude and phase of the probe beam, relative to the pump beam, is the measured quantity. In the pulsed configurations, often referred to as time-domain thermoreflectance (TDTR), the amplitude and phase of the probe beam is measured while either the modulation frequency of the pump beam or the delay between pulses is varied. See C. A. Paddock et al., Transient thermoreflectance from thin metal films, Journal of Applied Physics, 60 (1986) 285-290; W. Capinski, H. Maris et al., Thermal-conductivity measurements of GaAs/AlAs superlattices using a picosecond optical pump-and-probe technique, Physical Review B, 59 (1999) 8105; L. Belliard et al., Determination of the thermal diffusivity of bulk and layered samples by time domain thermoreflectance: Interest of lateral heat diffusion investigation in nanoscale time range, Journal of Applied Physics, 117 (2015) 065306; and K. C. Collins et al., Examining thermal transport through a frequency-domain representation of time-domain thermoreflectance data, Review of Scientific Instruments, 85 (2014) 124903.
In the non-pulsed configuration, often referred to as frequency-domain thermoreflectance (FDTR), the amplitude and phase of the probe beam is measured while the modulation frequency of the pump beam is varied or the distance between the pump and probe is varied. See D. Fournier et al., Lateral heat diffusion in layered structures: Theory and photothermal experiments, The European Physical Journal Special Topics, 153 (2008) 69-73; J. A. Malen et al., Optical measurement of thermal conductivity using fiber aligned frequency domain thermoreflectance, Journal of Heat Transfer, 133 (2011) 081601; B. Li et al., Thermal characterization of film-on-substrate systems with modulated thermoreflectance microscopy, Review of scientific instruments, 71 (2000) 2154-2160; and B. Li et al., Complete thermal characterization of film-on-substrate system by modulated thermoreflectance microscopy and multiparameter fitting, Journal of Applied Physics, 86 (1999) 5314-5316. A thorough summary of both TDTR and FDTR has been provide by Schmidt. See A. J. Schmidt, Pump-probe thermoreflectance, Annual Review of Heat Transfer, 16 (2013).
The periodic heating of the pump beam induces a periodic thermal response in the sample which is often referred to as thermal waves. There are many thermal measurement techniques that utilize this type of periodic heating from a modulated laser to generate thermal waves. See D. P. Almond et al., Photothermal science and techniques, Springer Science & Business Media, 1996. The detection of these thermal waves by use of the reflected pump beam is what distinguishes FDTR from other techniques.
There are many variations in the experimental setups of FDTR systems, which, applicants of the present disclosure categorize into two cases. In the first case the pump and probe beam are located concentrically on the sample and in the second case the two beams are offset from each other. Often a scanning technique is used where the probe beam measures the surface temperature at various distances from the pump beam. See G. Langer et al., Thermal conductivity of thin metallic films measured by photothermal profile analysis, Review of Scientific Instruments, 68 (1997) 1510-1513; A. Salazar et al., Thermal diffusivity measurements using linear relations from photothermal wave experiments, Review of scientific instruments, 65 (1994) 2896-2900; and A. Maznev et al., Thermal wave propagation in thin films on substrates, Journal of applied physics, 78 (1995) 5266-5269. FIG. 1 illustrates a diagram for a traditional MOR system using spatial scanning of the probe beam. Recently, an analogous technique has been developed that measures the temperature amplitude and phase at a given radius from the pump beam, for a range of frequencies. See Z. Hua et al., The study of frequency-scan photothermal reflectance technique for thermal diffusivity measurement, Review of Scientific Instruments, 86 (2015) 054901. This configuration has some advantages over the experimental setup required for a scanning probe beam.
Optical fiber based MOR systems have been developed in the past by Yarai et al. See A. Yarai, T. Nakanishi, Laptop photothermal reflectance measurement instrument assembled with optical fiber components, Review of scientific instruments, 78 (2007) 054903. Other photothermal techniques have employed the use of fiber optics in both delivering the heating power and in the sensing technique. See O. Eyal et al., Fiber-optic pulsed photothermal radiometry for fast surface-temperature measurements, Applied optics, 37 (1998) 5945-5950; P. Beard et al., Optical fiber photoacoustic—photothermal probe, Optics letters, 23 (1998) 1235-1237; and J. Laufer et al., Comparison of the photothermal sensitivity of an interferometric optical fiber probe with pulsed photothermal radiometry, Review of scientific instruments, 73 (2002) 3345-3352. Others have used fiber components to align the pump and probe beams or to improve accuracy of the measurement. See J. A. Malen et al., Optical measurement of thermal conductivity using fiber aligned frequency domain thermoreflectance, Journal of Heat Transfer, 133 (2011) 081601W.S; and Capinski et al., Improved apparatus for picosecond pump-and-probe optical measurements, Review of Scientific Instruments, 67 (1996) 2720-2726. In these fiber-based MOR systems, only concentric pump and probe configurations, where both the pump and probe beam are ultimately transmitted to the sample in a single fiber, have been explored.